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Use a model to subtract. Draw a picture to illustrate your model.

1 1 3 2 3


A circle divided into three sections, two of which are shaded.

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Use a model to subtract. Draw a picture to illustrate your model.

1 1 5 4 5


A circle divided into 5 sections, 2 of which are shaded.

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Subtract mixed numbers with a common denominator

Now we will subtract mixed numbers without using a model. But it may help to picture the model in your mind as you read the steps.

    Subtract mixed numbers with common denominators.

  1. Rewrite the problem in vertical form.
  2. Compare the two fractions.
    • If the top fraction is larger than the bottom fraction, go to Step 3.
    • If not, in the top mixed number, take one whole and add it to the fraction part, making a mixed number with an improper fraction.
  3. Subtract the fractions.
  4. Subtract the whole numbers.
  5. Simplify, if possible.

Find the difference: 5 3 5 2 4 5 .

Solution

.
Rewrite the problem in vertical form. .
Since 3 5 is less than 4 5 , take 1 from the 5 and add it to the 3 5 : ( 5 5 + 3 5 = 8 5 ) .
Subtract the fractions. .
Subtract the whole parts.
The result is in simplest form.
.

Since the problem was given with mixed numbers, we leave the result as mixed numbers.

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Find the difference: 6 4 9 3 7 9 .

2 2 3

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Find the difference: 4 4 7 2 6 7 .

1 5 7

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Just as we did with addition, we could subtract mixed numbers by converting them first to improper fractions. We should write the answer in the form it was given, so if we are given mixed numbers to subtract we will write the answer as a mixed number    .

Subtract mixed numbers with common denominators as improper fractions.

Step 1. Rewrite the mixed numbers as improper fractions.

Step 2. Subtract the numerators.

Step 3. Write the answer as a mixed number, simplifying the fraction part, if possible.

Find the difference by converting to improper fractions:

9 6 11 7 10 11 .

Solution

9 6 11 7 10 11
Rewrite as improper fractions. 105 11 87 11
Subtract the numerators. 18 11
Rewrite as a mixed number. 1 7 11
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Find the difference by converting the mixed numbers to improper fractions:

6 4 9 3 7 9 .

2 2 3

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Find the difference by converting the mixed numbers to improper fractions:

4 4 7 2 6 7 .

1 5 7

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Add and subtract mixed numbers with different denominators

To add or subtract mixed numbers with different denominators, we first convert the fractions to equivalent fractions with the LCD. Then we can follow all the steps we used above for adding or subtracting fractions with like denominators.

Add: 2 1 2 + 5 2 3 .

Solution

Since the denominators are different, we rewrite the fractions as equivalent fractions with the LCD, 6 . Then we will add and simplify.

There are three vertical addition problems. The first shows 2 and 1 half plus 5 and 2 thirds. There is an arrow pointing to the next. This one shows 2 and 1 times a red 3 over 2 times a red 3, with an arrow pointing to the top red 3 that says, “Change into equivalent,” plus 5 and 2 times a red 2 over 3 times a red 2. There is an arrow pointing to the next. This one shows 2 and 3 sixths plus 5 and 4 sixths equals 7 and 7 sixths. Below are instructions to add and rewrite in simplest form. There is an arrow pointing to a red 8 and 1 sixth.

We write the answer as a mixed number because we were given mixed numbers in the problem.

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Add: 1 5 6 + 4 3 4 .

6 7 12

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Add: 3 4 5 + 8 1 2 .

12 3 10

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Subtract: 4 3 4 2 7 8 .

Solution

Since the denominators of the fractions are different, we will rewrite them as equivalent fractions with the LCD 8 . Once in that form, we will subtract. But we will need to borrow 1 first.

There are four vertical subtraction problems. The first shows 4 and 3 fourths minus 2 and 7 eighths. There is an arrow pointing to the next. This shows 4 and 3 times a red 2 over 4 times a red 2, with an arrow above saying, “change into equivalent,” minus 2 and 7 eighths. There is an arrow pointing to the next. This shows 4 and 6 eighths minus 2 and 7 eighths. There is an arrow pointing to the next. It says to borrow 1 whole from the 4, since we cannot subtract 7 eighths from 6 eighths, and shows 3 and 14 eighths minus 2 and 7 eighths equals 1 and 7 eighths.

We were given mixed numbers, so we leave the answer as a mixed number.

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Find the difference: 8 1 2 3 4 5 .

4 7 10

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Find the difference: 4 3 4 1 5 6 .

2 11 12

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Subtract: 3 5 11 4 3 4 .

Solution

We can see the answer will be negative since we are subtracting 4 from 3 . Generally, when we know the answer will be negative it is easier to subtract with improper fractions rather than mixed numbers.

3 5 11 4 3 4
Change to equivalent fractions with the LCD. 3 5 · 4 11 · 4 4 3 · 11 4 · 11

3 20 44 4 33 44
Rewrite as improper fractions. 152 44 209 44
Subtract. 57 44
Rewrite as a mixed number. −1 13 44
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Source:  OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9
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